In the last decade, there has been a substantial amount of research in finding routing algorithms designed specifically to run on real-world graphs. In 2010, Abraham et al. showed upper bounds on the query time in terms of a graph’s highway dimension and diameter for the current fastest routing algorithms, including contraction hierarchies, transit node routing, and hub labeling. In this paper,...

Server based route planning in road networks is now powerful enough to find quickest paths in a matter of milliseconds, even if detailed information on time-dependent travel times is taken into account. However this requires huge amounts of memory on each query server and hours of preprocessing even for a medium sized country like Germany. This is a problem since global internet companies would...

Data Warehouses facilitate multi-dimensional analysis of data from various data sources. While the original data sources are often heterogeneous, current modeling and implementation techniques discard and, thus, cannot exploit these heterogeneities. In this paper we introduce Hetero-Homogeneous Hierarchies to model dimension hierarchies and cubes with inherent heterogeneities. Hetero-homogeneou...

We prove that the existential theory of the Turing degrees, in the language with Turing reduction, 0, and unary relations for the classes in the generalized high/low hierarchy, is decidable.

Recently, Sanders and Schultes presented a shortest path algorithm, named Highway Hierarchies, for fast point-to-point shortest path queries. They report extremely quick average queries on the road network of USA. We consider the I/O efficiency of the algorithm and investigate how a good graph layout affects the average query time. We experiment with a few layout heuristics and obtain a speed-u...

We present two methods to compress the description of a route in a road network, i.e., of a path in a directed graph. The first method represents a path by a sequence of via edges. The subpaths between the via edges have to be unique shortest paths. Instead of via edges also via nodes can be used, though this requires some simple preprocessing. The second method uses contraction hierarchies to ...

We prove that the join of two sets may actually fall into a lower level of the extended low hierarchy [BBS86] than either of the sets. In particular, there exist sets that are not in the second level of the extended low hierarchy, EL2, yet their join is in EL2. That is, in terms of extended lowness, the join operator can lower complexity. Since in a strong intuitive sense the join does not lowe...

We present a new speedup technique for route planning that exploits the hierarchy inherent in real world road networks. Our algorithm preprocesses the eight digit number of nodes needed for maps of the USA or Western Europe in a few hours using linear space. Shortest (i.e. fastest) path queries then take around eight milliseconds to produce exact shortest paths. This is about 2 000 times faster...

We say that a computably enumerable (c.e.) degree b is a Lachlan nonsplitting base (LNB), if there is a computably enumerable degree a such that a > b, and for any c.e. degrees w,v ≤ a, if a ≤ w ∨ v ∨ b then either a ≤ w ∨ b or a ≤ v ∨ b. In this paper we investigate the relationship between bounding and nonbounding of Lachlan nonsplitting bases and the high /low hierarchy. We prove that there ...

Efficiently computing fast paths in large scale dynamic road networks (where dynamic traffic information is known over a part of the network) is a practical problem faced by several traffic information service providers who wish to offer a realistic fast path computation to GPS terminal enabled vehicles. The heuristic solution method we propose is based on a highway hierarchy-based shortest pat...